Towards Constraints on the Epoch of Reionization: a Phenomenological Approach
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Group Problems #22 - Solutions
Group Problems #22 - Solutions Friday, October 21 Problem 1 Ritz Combination Principle Show that the longest wavelength of the Balmer series and the longest two wavelengths of the Lyman series satisfy the Ritz Combination Principle. The wavelengths corresponding to transitions between two energy levels in hydrogen is given by: n2 λ = λlimit 2 2 ; (1) n − n0 where n0 = 1 for the Lyman series, n0 = 2 for the Balmer series, and λlimit = 91:1 nm for the Lyman series and λlimit = 364:5 nm for the Balmer series. Inspection of this equation shows that the longest wavelength corresponds to the transition between n = n0 and n = n0 + 1. Thus, for the Lyman series, the longest two wavelengths are λ12 and λ13. For the Balmer series, the longest wavelength is λ23. The Ritz combination principle states that certain pairs of observed frequencies from the hydrogen spectrum add together to give other observed frequencies. For this particular problem, we then have: ν12 + ν23 = ν13 =) h(ν12 + ν23) = hν13 (2) 1 1 1 =) hc + = hc (3) λ12 λ23 λ13 1 1 1 =) + = : (4) λ12 λ23 λ13 Inverting Eqn. 1 above gives: 2 2 2 1 1 n − n0 1 n0 = 2 = 1 − 2 : (5) λ λlimit n λlimit n To calculate 1/λ12 and 1/λ13, we use the Lyman series numbers and find 1/λ12 = −1 −1 3=(4 ∗ 91:1) = 0:00823 nm and 1/λ13 = 8=(9 ∗ 91:1) = 0:00976 nm . To compute 1/λ23, we use the Balmer series numbers and find 1/λ23 = 5=(9 ∗ 364:5) = 0:00152 −1 nm . -
Report from the Dark Energy Task Force (DETF)
Fermi National Accelerator Laboratory Fermilab Particle Astrophysics Center P.O.Box 500 - MS209 Batavia, Il l i noi s • 60510 June 6, 2006 Dr. Garth Illingworth Chair, Astronomy and Astrophysics Advisory Committee Dr. Mel Shochet Chair, High Energy Physics Advisory Panel Dear Garth, Dear Mel, I am pleased to transmit to you the report of the Dark Energy Task Force. The report is a comprehensive study of the dark energy issue, perhaps the most compelling of all outstanding problems in physical science. In the Report, we outline the crucial need for a vigorous program to explore dark energy as fully as possible since it challenges our understanding of fundamental physical laws and the nature of the cosmos. We recommend that program elements include 1. Prompt critical evaluation of the benefits, costs, and risks of proposed long-term projects. 2. Commitment to a program combining observational techniques from one or more of these projects that will lead to a dramatic improvement in our understanding of dark energy. (A quantitative measure for that improvement is presented in the report.) 3. Immediately expanded support for long-term projects judged to be the most promising components of the long-term program. 4. Expanded support for ancillary measurements required for the long-term program and for projects that will improve our understanding and reduction of the dominant systematic measurement errors. 5. An immediate start for nearer term projects designed to advance our knowledge of dark energy and to develop the observational and analytical techniques that will be needed for the long-term program. Sincerely yours, on behalf of the Dark Energy Task Force, Edward Kolb Director, Particle Astrophysics Center Fermi National Accelerator Laboratory Professor of Astronomy and Astrophysics The University of Chicago REPORT OF THE DARK ENERGY TASK FORCE Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation for its existence or magnitude. -
Observations of the Lyman Series Forest Towards the Redshift 7.1 Quasar ULAS J1120+0641 R
A&A 601, A16 (2017) Astronomy DOI: 10.1051/0004-6361/201630258 & c ESO 2017 Astrophysics Observations of the Lyman series forest towards the redshift 7.1 quasar ULAS J1120+0641 R. Barnett1, S. J. Warren1, G. D. Becker2, D. J. Mortlock1; 3; 4, P. C. Hewett5, R. G. McMahon5; 6, C. Simpson7, and B. P. Venemans8 1 Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK e-mail: [email protected] 2 Department of Physics & Astronomy, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA 3 Department of Mathematics, Imperial College London, London SW7 2AZ, UK 4 Department of Astronomy, Stockholm University, Albanova, 10691 Stockholm, Sweden 5 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK 6 Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK 7 Gemini Observatory, Northern Operations Center, N. A’ohoku Place, Hilo, HI 96720, USA 8 Max-Planck Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany Received 15 December 2016 / Accepted 9 February 2017 ABSTRACT We present a 30 h integration Very Large Telescope X-shooter spectrum of the Lyman series forest towards the z = 7:084 quasar ULAS J1120+0641. The only detected transmission at S=N > 5 is confined to seven narrow spikes in the Lyα forest, over the redshift range 5:858 < z < 6:122, just longward of the wavelength of the onset of the Lyβ forest. There is also a possible detection of one further unresolved spike in the Lyβ forest at z = 6:854, with S=N = 4:5. -
Arxiv:1707.01004V1 [Astro-Ph.CO] 4 Jul 2017
July 5, 2017 0:15 WSPC/INSTRUCTION FILE coc2ijmpe International Journal of Modern Physics E c World Scientific Publishing Company Primordial Nucleosynthesis Alain Coc Centre de Sciences Nucl´eaires et de Sciences de la Mati`ere (CSNSM), CNRS/IN2P3, Univ. Paris-Sud, Universit´eParis–Saclay, Bˆatiment 104, F–91405 Orsay Campus, France [email protected] Elisabeth Vangioni Institut d’Astrophysique de Paris, UMR-7095 du CNRS, Universit´ePierre et Marie Curie, 98 bis bd Arago, 75014 Paris (France), Sorbonne Universit´es, Institut Lagrange de Paris, 98 bis bd Arago, 75014 Paris (France) [email protected] Received July 5, 2017 Revised Day Month Year Primordial nucleosynthesis, or big bang nucleosynthesis (BBN), is one of the three evi- dences for the big bang model, together with the expansion of the universe and the Cos- mic Microwave Background. There is a good global agreement over a range of nine orders of magnitude between abundances of 4He, D, 3He and 7Li deduced from observations, and calculated in primordial nucleosynthesis. However, there remains a yet–unexplained discrepancy of a factor ≈3, between the calculated and observed lithium primordial abundances, that has not been reduced, neither by recent nuclear physics experiments, nor by new observations. The precision in deuterium observations in cosmological clouds has recently improved dramatically, so that nuclear cross sections involved in deuterium BBN need to be known with similar precision. We will shortly discuss nuclear aspects re- lated to BBN of Li and D, BBN with non-standard neutron sources, and finally, improved sensitivity studies using Monte Carlo that can be used in other sites of nucleosynthesis. -
The Reionization of Cosmic Hydrogen by the First Galaxies Abstract 1
David Goodstein’s Cosmology Book The Reionization of Cosmic Hydrogen by the First Galaxies Abraham Loeb Department of Astronomy, Harvard University, 60 Garden St., Cambridge MA, 02138 Abstract Cosmology is by now a mature experimental science. We are privileged to live at a time when the story of genesis (how the Universe started and developed) can be critically explored by direct observations. Looking deep into the Universe through powerful telescopes, we can see images of the Universe when it was younger because of the finite time it takes light to travel to us from distant sources. Existing data sets include an image of the Universe when it was 0.4 million years old (in the form of the cosmic microwave background), as well as images of individual galaxies when the Universe was older than a billion years. But there is a serious challenge: in between these two epochs was a period when the Universe was dark, stars had not yet formed, and the cosmic microwave background no longer traced the distribution of matter. And this is precisely the most interesting period, when the primordial soup evolved into the rich zoo of objects we now see. The observers are moving ahead along several fronts. The first involves the construction of large infrared telescopes on the ground and in space, that will provide us with new photos of the first galaxies. Current plans include ground-based telescopes which are 24-42 meter in diameter, and NASA’s successor to the Hubble Space Telescope, called the James Webb Space Telescope. In addition, several observational groups around the globe are constructing radio arrays that will be capable of mapping the three-dimensional distribution of cosmic hydrogen in the infant Universe. -
DARK AGES of the Universe the DARK AGES of the Universe Astronomers Are Trying to fill in the Blank Pages in Our Photo Album of the Infant Universe by Abraham Loeb
THE DARK AGES of the Universe THE DARK AGES of the Universe Astronomers are trying to fill in the blank pages in our photo album of the infant universe By Abraham Loeb W hen I look up into the sky at night, I often wonder whether we humans are too preoccupied with ourselves. There is much more to the universe than meets the eye on earth. As an astrophysicist I have the privilege of being paid to think about it, and it puts things in perspective for me. There are things that I would otherwise be bothered by—my own death, for example. Everyone will die sometime, but when I see the universe as a whole, it gives me a sense of longevity. I do not care so much about myself as I would otherwise, because of the big picture. Cosmologists are addressing some of the fundamental questions that people attempted to resolve over the centuries through philosophical thinking, but we are doing so based on systematic observation and a quantitative methodology. Perhaps the greatest triumph of the past century has been a model of the uni- verse that is supported by a large body of data. The value of such a model to our society is sometimes underappreciated. When I open the daily newspaper as part of my morning routine, I often see lengthy de- scriptions of conflicts between people about borders, possessions or liberties. Today’s news is often forgotten a few days later. But when one opens ancient texts that have appealed to a broad audience over a longer period of time, such as the Bible, what does one often find in the opening chap- ter? A discussion of how the constituents of the universe—light, stars, life—were created. -
Dermining the Photon Budget of Galaxies During Reionization with Numerical Simulations, and Studying the Impact of Dust Joseph Lewis
Who reionized the Universe ? : dermining the photon budget of galaxies during reionization with numerical simulations, and studying the impact of dust Joseph Lewis To cite this version: Joseph Lewis. Who reionized the Universe ? : dermining the photon budget of galaxies during reioniza- tion with numerical simulations, and studying the impact of dust. Astrophysics [astro-ph]. Université de Strasbourg, 2020. English. NNT : 2020STRAE041. tel-03199136 HAL Id: tel-03199136 https://tel.archives-ouvertes.fr/tel-03199136 Submitted on 15 Apr 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNIVERSITÉ DE STRASBOURG ÉCOLE DOCTORALE 182 UMR 7550, Observatoire astronomique de Strasbourg THÈSE présentée par : Joseph Lewis soutenue le : 25 septembre 2020 pour obtenir le grade de : Docteur de l’université de Strasbourg Discipline/ Spécialité : Astrophysique Qui a réionisé l’Univers ? Détermination par la simulation numérique du budget de photons des galaxies pendant l’époque de la Réionisation, et étude de l’impact des poussières THÈSE dirigée par : M. AUBERT Dominique Professeur des universités, Université de Strasbourg RAPPORTEURS : M. GONZALES Mathias Maître de conférences, Université de Paris M. LANGER Mathieu Professeur des universités, Université Paris-Saclay AUTRES MEMBRES DU JURY : M. -
Determining the Redshift of Reionization from the Spectra Of
CORE Metadata, citation and similar papers at core.ac.uk Provided by CERN Document Server Determining the Redshift of Reionization From the Sp ectra of High{Redshift Sources 1;2 1 Zoltan Haiman and Abraham Lo eb ABSTRACT The redshift at which the universe was reionized is currently unknown. We examine the optimal strategy for extracting this redshift, z , from the sp ectra of reion early sources. For a source lo cated at a redshift z beyond but close to reionization, s 32 (1 + z ) < (1 + z ) < (1 + z ), the Gunn{Peterson trough splits into disjoint reion s reion 27 Lyman , , and p ossibly higher Lyman series troughs, with some transmitted ux in b etween these troughs. We show that although the transmitted ux is suppressed considerably by the dense Ly forest after reionization, it is still detectable for suciently bright sources and can b e used to infer the reionization redshift. The Next Generation Space Telescop e will reach the sp ectroscopic sensitivity required for the detection of such sources. Subject headings: cosmology: theory { quasars: absorption lines { galaxies: formation {intergalactic medium { radiative transfer Submitted to The Astrophysical Journal, July 1998 1. Intro duction The standard Big Bang mo del predicts that the primeval plasma recombined and b ecame predominantly neutral as the universe co oled b elow a temp erature of several thousand degrees at 3 a redshift z 10 (Peebles 1968). Indeed, the recent detection of Cosmic Microwave Background (CMB) anisotropies rules out a fully ionized intergalactic medium (IGM) beyond z 300 (Scott, Silk & White 1995). However, the lack of a Gunn{Peterson trough (GP, Gunn & Peterson 1965) in the sp ectra of high{redshift quasars (Schneider, Schmidt & Gunn 1991) and galaxies (Franx et < al. -
Unique Astrophysics in the Lyman Ultraviolet
Unique Astrophysics in the Lyman Ultraviolet Jason Tumlinson1, Alessandra Aloisi1, Gerard Kriss1, Kevin France2, Stephan McCandliss3, Ken Sembach1, Andrew Fox1, Todd Tripp4, Edward Jenkins5, Matthew Beasley2, Charles Danforth2, Michael Shull2, John Stocke2, Nicolas Lehner6, Christopher Howk6, Cynthia Froning2, James Green2, Cristina Oliveira1, Alex Fullerton1, Bill Blair3, Jeff Kruk7, George Sonneborn7, Steven Penton1, Bart Wakker8, Xavier Prochaska9, John Vallerga10, Paul Scowen11 Summary: There is unique and groundbreaking science to be done with a new generation of UV spectrographs that cover wavelengths in the “Lyman Ultraviolet” (LUV; 912 - 1216 Å). There is no astrophysical basis for truncating spectroscopic wavelength coverage anywhere between the atmospheric cutoff (3100 Å) and the Lyman limit (912 Å); the usual reasons this happens are all technical. The unique science available in the LUV includes critical problems in astrophysics ranging from the habitability of exoplanets to the reionization of the IGM. Crucially, the local Universe (z ≲ 0.1) is entirely closed to many key physical diagnostics without access to the LUV. These compelling scientific problems require overcoming these technical barriers so that future UV spectrographs can extend coverage to the Lyman limit at 912 Å. The bifurcated history of the Space UV: Much the course of space astrophysics can be traced to the optical properties of ozone (O3) and magnesium fluoride (MgF2). The first causes the space UV, and the second divides the “HST UV” (1150 - 3100 Å) and the “FUSE UV” (900 - 1200 Å). This short paper argues that some critical problems in astrophysics are best solved by a future generation of high-resolution UV spectrographs that observe all wavelengths between the Lyman limit and the atmospheric cutoff. -
Arxiv:1704.03416V1 [Astro-Ph.GA] 11 Apr 2017 2
Physics of Lyα Radiative Transfer Mark Dijkstra (Institute of Theoretical Astrophysics, University of Oslo) (Dated: April 7, 2017) Lecture notes for the 46th Saas-Fee winterschool, 13-19 March 2016, Les Diablerets, Switzerland. See http://obswww.unige.ch/Courses/saas-fee-2016/ arXiv:1704.03416v1 [astro-ph.GA] 11 Apr 2017 2 Contents 1. Preface 3 2. Introduction 3 3. The Hydrogen Atom and Introduction to Lyα Emission Mechanisms 4 3.1. Hydrogen in our Universe 4 3.2. The Hydrogen Atom: The Classical & Quantum Picture 6 3.3. Radiative Transitions in the Hydrogen Atom: Lyman, Balmer, ..., Pfund, .... Series 8 3.4. Lyα Emission Mechanisms 9 4. A Closer Look at Lyα Emission Mechanisms & Sources 10 4.1. Collisions 10 4.2. Recombination 13 5. Astrophysical Lyα Sources 14 5.1. Interstellar HII Regions 14 5.2. The Circumgalactic/Intergalactic Medium (CGM/IGM) 16 6. Step 1 Towards Understanding Lyα Radiative Transfer: Lyα Scattering Cross-section 22 6.1. Interaction of a Free Electron with Radiation: Thomson Scattering 22 6.2. Interaction of a Bound Electron with Radiation: Lorentzian Cross-section 25 6.3. Interaction of a Bound Electron with Radiation: Relation to Lyα Cross-Section 26 6.4. Voigt Profile of Lyα Cross-Section 27 7. Step 2 Towards Understanding Lyα Radiative Transfer: The Radiative Transfer Equation 29 7.1. I: Absorption Term: Lyα Cross Section 30 7.2. II: Volume Emission Term 30 7.3. III: Scattering Term 30 7.4. IV: ‘Destruction’ Term 36 7.5. Lyα Propagation through HI: Scattering as Double Diffusion Process 38 8. -
Balmer and Rydberg Equations for Hydrogen Spectra Revisited
1 Balmer and Rydberg Equations for Hydrogen Spectra Revisited Raji Heyrovska Institute of Biophysics, Academy of Sciences of the Czech Republic, 135 Kralovopolska, 612 65 Brno, Czech Republic. Email: [email protected] Abstract Balmer equation for the atomic spectral lines was generalized by Rydberg. Here it is shown that 1) while Bohr's theory explains the Rydberg constant in terms of the ground state energy of the hydrogen atom, quantizing the angular momentum does not explain the Rydberg equation, 2) on reformulating Rydberg's equation, the principal quantum numbers are found to correspond to integral numbers of de Broglie waves and 3) the ground state energy of hydrogen is electromagnetic like that of photons and the frequency of the emitted or absorbed light is the difference in the frequencies of the electromagnetic energy levels. Subject terms: Chemical physics, Atomic physics, Physical chemistry, Astrophysics 2 An introduction to the development of the theory of atomic spectra can be found in [1, 2]. This article is divided into several sections and starts with section 1 on Balmer's equation for the observed spectral lines of hydrogen. 1. Balmer's equation Balmer's equation [1, 2] for the observed emitted (or absorbed) wavelengths (λ) of the spectral lines of hydrogen is given by, 2 2 2 λ = h B,n1[n2 /(n2 - n 1 )] (1) 2 where n1 and n2 (> n1) are integers with n1 having a constant value, hB,n1 = n1 hB is a constant for each series and hB is a constant. For the Lyman, Balmer, Paschen, Bracket and Pfund series, n1 = 1, 2, 3, 4 and 5 respectively. -
Spectra of Photoionized Regions 1. Introduction
Spectra of Photoionized Regions Friday, January 21, 2011 CONTENTS: 1. Introduction 2. Recombination Processes A. Overview B. Level networks C. Free-bound continuum D. Two-photon continuum E. Collisions 3. Additional Processes A. Lyman-α emission B. Helium processes C. Resonance fluorescence 4. Diagnostics A. Temperature B. Density C. Composition D. Star formation rates 1. Introduction Our next task is to consider the emitted spectrum from an H II region. This is one of the most important subjects observationally since spectroscopy provides our principal set of diagnostics on the physics occurring in the region. This material is (mostly) covered in Chapters 4 and 5 of Osterbrock & Ferland (on which most of these notes are based). The sources of emission we will consider fall into two categories: Cooling: Infrared fine structure lines Optical forbidden lines Free-free continuum Recombination: Free-bound continuum Recombination lines Two-photon continuua 1 Generally, the forbidden lines (optical or IR) come from metals, whereas the recombination features are proportional to abundance and arise mainly from H and He. Since the cooling radiation has already been discussed, we will focus on recombination and then proceed to diagnostics. 2. Recombination Processes A. OVERVIEW We first consider the case of recombination of hydrogen at very low densities where the collision rates are small, i.e. any hydrogen atom that forms can decay radiatively before any collision. Later on we will introduce collisions between particles (electrons, protons) with excited atoms. The recombination process at low density begins with a radiative recombination, H+ + e− → H0(nl) + γ , which populates an excited state of the hydrogen atom.